I was wondering if i can install a self-hosted server in different places on my network and make them communicate with each other (synchronize with each other) in case one site on my network goes down?
Different RU Servers cannot communicate with each other. If you are looking for a failover mechanism which would allow you to switch from server A to server B in case server A is down, you can use a "DNS trick". That is, you should use a DNS name for your server that points at server A's IP address. If server A is down, simply update your DNS record and point it at server B's IP address (the server should be running of course). These days DNS propagation literally takes seconds or minutes at the worst, so your remote connections will be quickly up and running again.